Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...) the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (shrink)

Popper and Miller (1983) have presented an argument purporting to establish the impossibility of inductive probability. Here I discuss critically their characterization of a deductive part of nondeductive support, a point that has not figured centrally in previous responses.

Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.